Running head: STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 1

Running head: STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 1 Developing Basic Fact Fluency Through Guided Strategy-Based Instruction to Lessen Student Anxiety by Laura K. Submitted in partial fulfillment of the requirements for the degree MASTER OF SCIENCE IN EDUCATION at BUFFALO STATE COLLEGE December 2013

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 2 Chapter One Introduction As the students filled back into the classroom after recess, each displayed a different set of emotions ranging from confidence, excitement and hopefulness to uncertainty, intimidation, frustration, terror and anxiety. The daily schedule displayed that it was now time for Fast Facts. I was serving as a long term substitute teacher in this particular second grade class. Twice, weekly, for the past four months, the regular classroom teacher had the students completing Fast Facts. Fast Facts consists of a sheet of eighteen basic addition or subtraction facts. The basic facts for addition refer to the combinations where both addends are less than ten. The basic subtraction facts are these that correspond to the addition facts. The goal was to correctly answer all of the problems in one minute. If the students were able to achieve the goal they moved on to the next test. After passing ten tests, the students progressed onto the next level; there were a total of thirty tests of increasing difficulty. As I began passing back the Fast Fact folders and the students had the opportunity to see how they had done on the last test, the range of emotions continued. Several students were excited having achieved the goal and making progress towards advancing to the next level. Other students were filled with frustration as they saw that they failed to complete the test, for some of them this was their fifth, sixth or even seventh time failing to achieve the goal. There were also those that were filled with disappointment and embarrassment, they were still working on level one. These were the students that sat and watched as their classmates completed level one and even a few had completed level two, receiving a piece of candy and stickers with each passing level, while they were left wondering if they would be able to get a piece of candy before the end of the year.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 3 After handing out the final folder, I started the timer and the students went to work. As that minute passed, I walked around the room, watching the students as they worked as quickly as they could to complete the page before the buzzer sounded. Those students that were already onto level three would often finish with fifteen or more seconds to spare and only required one or two attempts to pass each test, while some of those students on level one could hardly get through all of the problems and would require many retests in order to pass. Some of these students, despite being only two months away from finishing second grade were still counting on their fingers and drawing pictures to solve problems such as 5+6, taking up so much of their very limited time to complete the task. The alarm sounded and the students placed their papers in their folders and passed them forward, some of showed a glimmer of hope that this would be the last time they would take that test while others still showed disappointment knowing they had not finished all the problems. As the weeks continued, every Tuesday and Thursday, this same scenario replayed itself. After school I would sit, correcting these tests. There were a handful of students who, despite working on these tests for four months, were still only on test 8 or 9 of the thirty tests. The majority of the students were working on the last few test of level two, tests 16-19. There were also a small handful of students that were only a few tests away from completing all thirty tests. As the weeks continued, I wondered if the time spent testing the students, correcting the tests, stuffing the folders and the emotions the students faced during this process were worth it. I wondered if these tests that were meant to increase mathematical fluency working the way they should; did the low level students have strong, thoroughly developed mathematical strategies to help them with these tests; were the tests wasting the high achieving students time?

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 4 Purpose of the Study The purpose of this study was to examine the effects of timed testing for basic mathematical fact fluency on students, in particular the emotional effects and the fluency development effects of this testing method. The information gathered at the conclusion of this study will help develop a greater understanding on how teachers can better help and prepare their students to become more fluent masters of the basic mathematical facts. Research Question 1. What are the effects of fact drill on students feelings towards mathematics? Importance of the Study The acquisition of quick and accurate recall of the basic mathematical facts (addition, subtraction, multiplication and division) is an essential building block in all students development of mathematical concepts. In order to ensure that students attain this fluency, teachers need to be teaching and assessing their development of this skill effectively while fostering confidence and fondness rather than fear and anxiety for math.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 5 Chapter Two Literature Review A review of the literature advises against teaching basic facts through rote memorization and avoiding the use of rote drills for math facts until students have developed the substantial mathematical reasoning needed to understand those facts. Rote memorization does not foster development of fluent and proficient learners. Rote memorization can be difficult for learners resulting in feelings of anxiety, which works against learning mathematics. There are many researchers who support a different approach. The purpose of this literature review is to explore the research on guided strategy-based instruction for basic mathematical facts to lead to fact mastery and promote positive feelings towards math. This review will discuss the recent call for deeper understanding in mathematics instruction, the challenges of learning the basic mathematical facts and the benefits of a strategy-based instruction approach on students fact fluency and feelings towards mathematics as well as the strategy development phases. Finally, the role of the teacher in developing fact fluency in students, through guided strategy instruction will be discussed. Call for Deeper Understanding. Fluency with mathematical facts includes a deeper understanding of the concepts and efficient, appropriate, flexible, ready to use computational skills across a variety of applications (Baroody, 2006; Wallace & Gurganus, 2005). The National Council of Teachers of Mathematics (NCTM) is calling for students to learn mathematics with understanding, actively building new knowledge from experience and prior knowledge (NCTM, 2000, p. 10). Mathematics makes more sense and is easier for students to remember and apply when it is related to existing knowledge in meaningful ways. Learning basic mathematical facts through strategy-based instruction rather than rote memorization provides an efficient and accurate method for computing based on properties, prior knowledge

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 6 and number relationships that develops deeper understanding of the concepts (Wallace et al., 2005). Discovering patterns and relationships between operations, numbers and facts is essential for laying the groundwork to developing deeper understanding (Baroody, 2006; Flowers & Rubenstein, 2010). Developing deeper understanding of mathematical concepts through meaningful connections, between new and existing knowledge, leads to less errors, less forgetting, less information that has to be learned and ultimately, less anxiety towards math. Difficulties of Learning the Basic Facts. Understanding the basic facts, particularly multiplication requires higher-level thinking than addition or subtraction, making it more difficult to master (Wong & Evans, 2007). For example, when solving 3+7, one must just think about combining three and seven. In comparison, when solving 3x7, one must combine three seven times. This abstract thinking makes it difficult and frustrating for some students leading to feeling of anxiety towards math. Another obstacle that makes learning the facts challenging is the number of facts that students are expected to learn. There are one hundred number combinations, or facts, containing addends or factors that range from zero to nine, that need to be mastered on the addition and multiplication table. Then there are one hundred basic subtraction and division facts that correspond to the addition and multiplication facts. Discovering patterns relieves some of the difficulties of learning these four hundred basic facts and alleviates the negative emotions associated with the stress of trying to memorize them all individually (Van de Walle, Karp & Bay-Williams, 2010). Historically, students that had difficulty learning the basic facts were thought to have deficits, such as in-attentiveness, forgetfulness or being prone to confusion (Baroody, 2006). Research has proven that students difficulties are due to inadequate or inappropriate instruction

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 7 that is dependent on rote memorization (2006; Wallace et al., 2005). Struggling students lack of informal knowledge, such as experiences that allow them to understand composition and decomposition of numbers, makes learning through memorization difficult. Learning, with the focus on learning through memorization discourages looking for patterns and relationships, deflects efforts to reason out answers, and undermines interest in mathematics and confidence in mathematical ability (Baroody, 2006, p. 27). Without conceptual learning, strategic mathematical thinking, and a productive disposition, students will be unsuccessful at achieving fluency in the basic mathematics facts. Benefits of Strategy Instruction. Using a problem based approach and focusing on strategies will lead to development of fact mastery (Baroody, 2006; Wallace et al., 2005; Van de Walle et al., 2010). Through strategy-based instruction, students develop clear number sense by discovering patterns, building relationships, and creating a body of interconnected knowledge of numbers and how they operate or interact (2006, p. 24). This well-connected factual knowledge is easier for students to retain than isolated facts that have been memorized (2006). Students that develop connections between numbers and multiplication facts will be at an advantage over those that have not and in turn will be more comfortable when solving these problems quickly. These students will be able to use their knowledge and strategies to solve for forgotten solution (Wallace et al., 2005; Wong & Evans, 2007). For example, if a student forgets the product of eight and seven, they can use 4x7 and double it. A student would only be able to use this strategy if they have a clear, conceptual understanding of multiplication, as well as the number sense that the number eight can be broken apart. Allowing students to explore and investigate strategies promotes meaningful, inquiry based, purposeful instruction that results in children that have the ability to use basic knowledge

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 8 efficiently, appropriately and flexibly (Baroody, 2006, p. 30) while also developing problem solving and reasoning skills and increasing confidence in their abilities (Flowers & Rubenstein, 2010). Strategy Development. Proficiency in the basic facts is a developmental process in which students move through stages, starting with the easiest strategies and moving towards the more advanced, eventually reaching automatic retrieval (Wallace et al., 2005; Wong et al., 2007). Students begin by making equal groups, drawing pictures and counting manipulatives, then advancing to skip counting and then understanding the properties of addition, subtraction, multiplication and division. As children acquire new strategies, they tend to abandon older, slower and less accurate ones (2007). Instruction must help students move through these phases without rushing them. In order to acquire these strategies, students need to be given time to explore and discover patterns and relationships on their own. Children are intrinsically motivated to make sense of the world and thus, look for regularities (Baroody, 2006, p.25). Children can and will discover patterns that can help them solve the basic problems. Uncovering relationships provides a foundation for strategies that will help students remember facts. After allowing the students time to explore on their own, students should be encouraged to discuss with their classmates, the ways they used reasoning strategies to determine the basic facts (Van de Walle et al., 2010). More structured activities may be needed for less obvious strategies. Students that are not given the time to explore and discuss relationships and patterns between numbers will be less likely to develop conceptual understand and the clear number sense required in becoming proficient and fluent in the facts. Therefore, classroom instruction plays a key role in students development towards mastery.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 9 Role of the Teacher. Teachers should address the basic facts in a way that encourages and promotes mastery. Van de Walle et al, (2010) explains the sequence in which facts should be introduced to increase students proficiency in learning and recalling these facts. Teachers need to plan experiences that provide students the opportunity to advance from counting to strategies to recall. When fostering fact fluency, a teacher should use a teach-for-understanding approach. This requires that the teacher be patient, helping students to construct number sense by encouraging them to invent, share and refine formal strategies (Baroody, 2006, p. 29). Students need to be given time to gradually build up ideas such as composition and decomposition of numbers. Teachers need to encourage students to construct reasoning strategies, look for relationships and build off of prior knowledge. Relating unknown combinations to previously learned ones can greatly reduce the amount of practice needed to master combinations (Baroody, 2006, p. 29). Teachers should allow for the use of any efficient strategy, encouraging flexibility in using a variety of strategies (Van de Walle et al., 2010). Effective strategies can be taught to children that are using immature approaches, such as finger counting (Wallace & Gurganus, 2005). Once students have discovered patterns and relationships and effective, flexible strategies, the teacher s role is to encourage automaticity, through purposeful practice, rather than drilling isolated facts (Baroody, 2006). A teacher that encourages discovery of patterns, invention and refinement of informal strategies and implements purposeful practice will promote understanding, fluency and mastery of the basic facts. Conclusion Teaching for mastery of the basic mathematic facts no longer means rote memorization of basic facts and testing of fluency with timed test, rather an emphasis on strategy instruction

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 10 that helps students organize facts into coherent knowledge networks (Baroody, 2006; Wallace et al., 2005; Wong et al., 2007; Flowers et al., 2010; Woodward, 2006; Van de Walle et al., 2010). Making connections between computational fluency and conceptual understanding is important for all students in order to achieve basic fact mastery. Teachers should teacher for deep understanding and encourage the use of personal strategies that are efficient, accurate and flexible in order to ensure success for students in learning the facts and developing automaticity of the basic facts. As a result, students will be more relaxed during timed testing situations and will be more confident in their mathematical ability.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 11 Chapter Three Overview A qualitative research design was used to collect data from six elementary aged students. In this study, the researcher examined the emotional effects and the effects on fluency development that result from timed testing for basic mathematical fact fluency through the use of audio clips from focus group interviews (Creswell, 2007), face-to-face observations and field notes of these meetings. The data was analyzed using open coding (Corbin & Strauss, 2008). This chapter will describe the participants, research site, role of the researcher and finally, the data collection and analysis techniques that were utilized. Methodology Participant(s). Six elementary aged students were surveyed to determine their experiences with and emotions towards timed mathematical fluency tests. The names of each of the participants of this study have all been given pseudonyms to protect their identity. Ruby, Sarah and John are all current third graders and Ethan, Mark and Molly are all current fourth graders at the same rural school. All of the students are white. The sample of students selected represents students with varying levels of mathematical ability. Site of study. The school that all of the participants attend is a small, rural school. The elementary school (K-5) has a total population of 700 students that consists of 87% white, 11% American Indian, 1% black and 1% Hispanic. Of the 700 students enrolled, 30% qualify for free or reduced lunch. The participants that were chosen to participate in this study all attend an after school child care program within the school district. This center provides services for twenty students. The center was the chosen location to conduct the interviews. The subjects were interviewed in

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 12 a quiet room away from other students and distractions including toys, the television, games and crafts. Role of the researcher. The researcher is a graduate student that is currently substitute teaching in the school that the participants attend and is serving as the assistant director at the child care center in which all the participants are enrolled. The researcher worked as a long term substitute teacher for all of the third grade participants during their second grade school year. For this study, the researcher assumed the role of participant observer. Plan to combat bias. In order to confront bias, it is important that the researcher keep an open, nonjudgmental mind to the views expressed by the participants, in particular when those views differ from what may be expected. As the researcher conducted the interviews, it is essential that the researcher remain objective, keeping a neutral stance on the topics discussed, and paying careful attention to not intervene with personal emotions or assumptions. Methods Data collection. The researcher collected data for this study through formal focus group interviews. During the interviews, the researcher also had the opportunity to complete face-toface observations and field notes of these observations. Copies of data collection materials for this study are located in the appendix. Interviews. Creswell (2007) suggests collecting data through focus group interviews. Focus group interviews are interviews that are conducted with several participants at once. The participants should be similar with and cooperative towards each of the other participants. For the purpose of this study, the student participants were interviewed in groups of three, separated by grade level. By participating in the interview as a group, rather than as individuals, the students may feel more comfortable and be more involved and open up. During this style of

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 13 interviewing it is particularly important that the researcher monitor individuals that dominate the conversation and also encourage all to participate (Creswell, 2007). Both interviews were audio recorded so that the researcher could refer after the interview was completed to transcribe the entire conversation. Data analysis. After completing the interview process and transcribing an account of the interview, the researcher analyzed the data by looking for and labeling any phenomena that occurred, making comparisons between responses from the six participants and grouping similarities and using the open coding procedures of Corbin et al. (2008) by breaking down and categorizing the responses, one question at a time. Several categories including: feelings of being rushed, feeling of nervousness and feelings of excitement, emerged from the open coding of the interview transcripts. Summary This chapter discussed the qualitative study that was conducted to collect data from six elementary aged students. Through this study, the researcher was able examine the emotional effects and the effects on fluency development that result from timed testing for basic mathematical fact fluency. The participants, research site, role of the researcher and finally, the data collection and analysis techniques that were utilized were described. The findings that resulted from this study will be discussed in the next chapter.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 14 Chapter Four Overview of Study The purpose of this study was to examine the effects of timed testing for basic mathematical fact fluency on students, in particular the emotional effects and the fluency development effects of this testing method. This is a topic that has gained my interest after a long term substitute teaching position in a second grade classroom in which the regular teacher had implemented timed testing. As the weeks progressed in this class, I noticed that many of the students portrayed feelings of anxiety, uncertainty and frustration whenever it was time to complete the biweekly tests. As I walked around the room, observing them race to complete the facts, I noticed that many of the frustrated students were the ones that were falling behind, having to constantly repeat level one or lower level two tests while some of their classmates were on to level three. Many of these students that were struggling to pass the lower levels seemed to never be able to complete the eighteen problems in a minute because they did not know any quicker way to arrive at the answer than to count their fingers, wasting their very limited time. I wondered if these tests, that were meant to increase mathematical fluency, worked the way they should; did the low level students have strong, thoroughly developed mathematical strategies to help them with these tests; were the tests wasting the high achieving students time? A qualitative research design was used to collect data from six elementary aged students. In this study, the researcher examined the emotional effects and the effects on fluency development that resulted from timed testing for basic mathematical fact fluency through the use of audio clips from focus group interviews, face-to-face observations and field notes of these meetings. After the data was collected, it was analyzed using open coding.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 15 Through the interviews and observation of the six participants, the researcher was able to see what the students thought the importance of the test were; their feelings towards timed testing; and the strategies that the students had to help get them past problems they had not yet mastered. At the completion of the study, the researcher concluded that the students that reported feeling scared or nervous before or during a timed mathematical fluency test had no strong strategy development to rely on when faced with an unknown fact and often resorted to finger counting. The students that reported feeling excited and confident were the ones that had a strong recollection of strategies they could call upon if faced with unknown facts. Assertion #1: Students understand that timed math tests help teachers to assess student knowledge Through the process of interviewing all of the participants, the researcher was able to gather that all participants believed that one of the reasons that their teachers have them take timed tests was to assess what facts the students have gained mastery in and which facts they still need to work on. Ruby, Sarah, Molly and Ethan all stated helping students get better as an additional reason for taking timed tests. Some of the other reasons that the students gave when asked why they had to take these types of tests can be seen in table 1. Table 1 Students beliefs for teachers to give students timed tests. Reasons Teacher Gives Timed Tests Number of Participants that Believe See what students know and what they don t 6/6 Help students get better 4/6 Work to keep students busy 1/6 Grades 2/6 Practice skill 2/6

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 16 Students want to focus on correctness rather than speed. One point that was also mentioned by the students was that the focus should be on knowing the facts, no matter how long it took. This idea can be summarized in the following quote from Sarah during the interview, It is not important to know them (the answers) so fast. We should be able to take our time and think so we can make sure that we get them right. This idea was also echoed by John, I don t know why they make you rush! and Ethan, I wish there was more time. These students realize that in their daily lives, if they are faced with a situation that would require them to solve a math problem, the focus should be on correctness rather than speed. Ethan offered an example, if you are at the store and you need to know how many pieces of candy are in two bags of candy, there is no reason to rush, you should take your time and get the right answer. The rushed nature of these tests competed with the kids notions of correctness over speed resulting in negative feelings towards these tests for most students, in particular, those at a lower ability level. Assertion #2: Students experience a diverse range of feelings during timed fluency testing During the interview, the participants described a range of emotions that they recalled feeling while taking timed tests in school. The most common feelings included being rushed and nervous. All of the participants responses are described in table 2. Table 2 Students feeling as they take timed math tests. Student Name Third Grade Ruby Sarah John Fourth Grade Molly Mark Ethan Feelings stressed, rushed rushed, nervous, crazy, excited rushed, scared, sad, crazy, nervous, stressed excited, nervous, rushed confident, love it, excited nervous

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 17 Students feel rushed. One comment that kept repeating over the course of all the interviews was the feeling of being rushed. The feeling of being rushed caused other negative feelings to emerge from the students, regardless off ability level. Ruby said, I don t like being timed, the clock makes me forget what I am doing and then I do bad. John and Sarah both expressed that being rushed made them feel crazy. John elaborated upon this idea by explaining that when he feels rushed he feels like he is going to blow up. He also described that when he is rushed, he can t take his time and it just doesn t feel right. Sarah does not understand why they (teachers) make you (students) rush. These students feelings of being rushed are amplified when they are facing more difficult problems, in particular, the subtraction and division problems with lager numbers. These are the problems that the students have a more difficult time with and typically get lower scores. Students feel nervous and scared. The feelings of nervousness and being scared are brought on by the fact that the students are given a limited time and they are afraid of the consequences if they do not finish in that time frame. Molly recollects feeling scared and nervous because of the limited time. Ethan recalls feeling so nervous that I (he) wanted to puke. John also experiences nervousness to the point of a stomach ache. Students feel excited. Mark feels very confident in his ability to complete timed math tests well. He says he loves it referring to when the teacher announces it is time to begin a timed test. He gets excited and thinks to himself, I got this in the bag! Molly recalls being excited for addition timed tests and some multiplication tests (problems with factors of 0,1,2,5,9,10), because those are easy. Now that she is onto multiplication and division she no longer gets excited. Sarah also recalls being excited when solving problems that she knows by heart.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 18 During the interview, the participants were also asked to describe feelings they observed their classmates having towards timed math tests. These feelings and the number of participants that identified having observed them are listed in table 3. The most common feeling the participants recall their classmates portraying include feelings of frustration, anger and nervousness, the least common included excitement and happiness. Table 3 Classmates feelings towards timed math tests observed by participants. Feelings Number of Participants that have Observed Behavior Frustration/Anger 4/6 Nervousness 5/6 Sadness/Upset 3/6 Excitement/Happiness 2/6 Assertion #3: Students are at varying levels of strategy development. As the students worked on identifying all of the strategies they could think of using when facing a problem that they did not know the answer to, the researcher determined that some of the students relied on very basic strategies such as counting up and finger counting while other students possess more complex strategies including close facts and number decomposition. All of the strategies described by each subject is listed in table 4. Table 4 Strategies students have knowledge of to help solve unknown facts. Student Name Third Grade Ruby Sarah Strategies -finger count -count up from larger number -finger count -count up from larger number -rewrite the problem vertically -turn around facts (8+6=6+8)

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 19 John Fourth Grade Molly Mark Ethan -close facts [ex: 8+6=(6+6)+2=(8+8)-2] -finger count -draw pictures -turn around facts (8+6=6+8) -finger count -skip count -close facts [8x6=(8x5)+8] -close facts [8x6=(8x5)+8] -number decomposition [8x6=(8x2)+(8x2)+(8x2)] -finger count -skip count -rhyming songs -turn around facts (8x6=6x8) Students have basic strategy development. Reviewing the strategies that the students shared, the researcher determined that three of the students have basic strategy development. Ruby, John and Ethan are all relying of simplistic strategies to solve problems. These strategies include finger counting, skip counting, drawing pictures and counting up from the larger number (addition). These strategies, particularly finger counting, drawing pictures and counting up can take some time to complete, using up a lot of that very limited time frame that the students described as being nervous about. Students have complex strategy development. The other three participants, Sarah, Molly and Mark all demonstrated knowledge of complex strategy development. Strategies that the researcher considers complex include using close facts and decomposing numbers to create known facts. Assertion #4: Students that have deeper strategy development are more confident in their abilities and more positive towards tests. During the interview, the researcher asked each of the participants what strategies they use during testing. Table 5 lists all the strategies that each student described using in a testing

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 20 situation along with their level of strategy development and their general feelings towards timed tests. Based on the results in this table the researcher concluded that students that have deeper strategy development make use of these strategies during testing and generally feel more positive feelings towards timed tests. Mark, at the end of the interview, when asked if he had any final thought to add, summarized this point by saying, Students should really learn to use strategies. Table 5 Student s level of strategy development, strategies described as being used during testing and general feelings towards timed tests. Student Name Strategy Development Strategy During Testing Third Grade Ruby basic -count up from larger number -finger count Sarah complex -finger count -close facts John basic -skip and return if time -finger count if time Fourth Grade Molly complex -look for repeats on test -close facts Mark complex -no strategies-memorized facts -decompose numbers Ethan basic -skip and return if time -finger count -guess Feelings Towards Testing stressed, rushed rushed, nervous, crazy, excited rushed, scared, sad, crazy, nervous, stressed excited, nervous, rushed confident, love it, excited nervous Summary of Findings Overall, this study suggests that students that are able to recognize and call upon a wide range of strategies to effectively solve mathematical problems are more relaxed and excited to complete timed tests and are also more confident in their math ability. On the other hand, students that do not have a vast collection of strategies to call upon when solving an unknown fact are more anxious, nervous and stressed when facing timed tests. The findings support the

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 21 importance of teachers using guided strategy instruction to help students have a command of as many good strategies as possible leading to the development of quick and accurate recall of the basic facts.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 22 References Baroody, A. J. (2006). Why children have difficulties mastering the basic number combinations and how to help them. Teaching children mathematics, 13(1), 22-31. Flowers, J. M., & Rubenstein, R. N. (2010). Multiplication fact fluency: Using doubles. Mathematics teaching in the middle school, 16(5), 296-301. National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, Va.: NCTM, 2000. Van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon. Wallace, A. H., & Gurganus, S. P. (2005). Teaching for mastery of multiplication. Teaching children mathematics, 12(1), 26-33. Wong, M., & Evans, D. (2007). Improving basic multiplication fact recall for primary school students. Mathematics education research journal, 19(1), 89-106. Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning disability quarterly, 29(4), 269-289.

STRATEGY INSTRUCTION TO LESSEN MATHEMATICAL ANXIETY 23 Appendix A: Interview Questions Give the student a timed test (addition or multiplication depending on ability). 1. Why do you think the teacher has you take these tests? What do you think the results tell the teacher? 2. How did you feel when it was time to take the test? 3. Do you ever notice how other students feel when taking the tests? Do you think it is harder for them than you? How can you tell? 4. What is your strategy for completing a timed test? (Mention anything noticed while they worked on timed test at the beginning of interview jumping around, looking for repeated problems, solving the easiest first ) What do you do when you get stuck on a problem? 5. If you don t finish a test, what do you think the teacher thinks? 6. How well do you think the test results show what you know? 7. If you were taking a timed test and you came to the problem (6+8 or 6x8 choose the more age appropriate problem) and you forgot the answer what would you do? What strategies do you know to help you figure out the answer? 8. Did you ever receive incentives (stickers, candy, special recognition board ) for doing well? How does it make you feel? Have you ever seen other kids receive incentives when you did not? How did you feel then?

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